House Robber III

The thief has found himself a new place for his thievery again. There is only one entrance to this area, called the “root.” Besides the root, each house has one and only one parent house. After a tour, the smart thief realized that “all houses in this place forms a binary tree”. It will automatically contact the police if two directly-linked houses were broken into on the same night.

Determine the maximum amount of money the thief can rob tonight without alerting the police.

Example 1:

  1.      3
  2.     / \
  3.    2   3
  4.     \   \ 
  5.      3   1

Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.

Example 2:

  1.      3
  2.     / \
  3.    4   5
  4.   / \   \ 
  5.  1   3   1

Maximum amount of money the thief can rob = 4 + 5 = 9.

Solution: